Noise Folding based on General Complete Perturbation in Compressed Sensing

This paper first present a new general completely perturbed compressed sensing (CS) model y=(A+E)(x+u)+e,called noise folding based on general completely perturbed CS system, where y ∈ Rm, u ∈ Rm, u 6= 0, e ∈ Rm, A ∈ Rm×n, m ≪ n, E ∈ Rm×n with incorporating general nonzero perturbation E to sensing matrix A and noise u into signal x simultaneously based on the standard CS model y=Ax+e. Our constructions mainly will whiten the new proposed CS model and explore into RIP, coherence for A+E of the new CS model after being whitened. Index Terms Compressed Sensing(CS), general perturbation, restricted isometry property(RIP), coherence